Bruce was born in Edinburgh on 28 December 1718, the son of Mary Balfour, daughter of Robert Balfour, 4th Lord Burleigh and Alexander Bruce of Kennet (1691-1747).
He served as Professor of Law of Nature and Nations at the University of Edinburgh (1758–64) and was appointed Sheriff-Depute of Stirling & Clackmannan in 1760.
[5][6] They had seven sons and one daughter, including his heir, Alexander (1755-1808) who was born in Edinburgh.
His brothers-in-law included James Stuart-Mackenzie (1719–1800), Alexander Abercromby, Lord Abercromby (1745–1795), James Edmonstone (d.1793) and Sir Lawrence Dundas, 1st Baronet (1712-1781) who had married his older sister Margaret (b.
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